Problem: Simplify the following expression: $q = \dfrac{10z}{7} + \dfrac{z}{8}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $7$ and $8$ $\lcm(7, 8) = 56$ $ q = \dfrac{8}{8} \cdot \dfrac{10z}{7} + \dfrac{7}{7} \cdot \dfrac{z}{8} $ $q = \dfrac{80z}{56} + \dfrac{7z}{56}$ $q = \dfrac{80z +7z}{56}$ $q = \dfrac{87z}{56}$